Influence of wall roughness on the slip behaviour of viscous fluids
Dorin Bucur, Eduard Feireisl, Šárka Nečasová · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2008
We consider the stationary equations of a general viscous fluid in an infinite (periodic) slab supplemented with Navier's boundary condition with a friction term on the upper part of the boundary. In addition, we assume that the upper part of the boundary is described by a graph of a function φε, where φε oscillates in a specific direction with amplitude proportional to ε. We identify the limit problem when ε → 0, in particular, the effective boundary conditions.